A nanosecond is a millionth of a second (I think ), so what makes up a nanosecond? A millennium is the largest (I think ) so what would be bigger?

The nansecond you mentioned is seconds, or 1 billionth of a second (a microsecond is a millionth of a second).

The smallest unit of time that I'm aware of is "Planck Time," which is about seconds.

Using official SI nomenclature, the largest unit of time would be the yottasecond, which is seconds, or about 32 quadrillion years, which is around 3 million times older than the age of the universe.